Heat olive oil in a large pot over medium heat. Add the onion and garlic, and sauté until slightly translucent.
Add the mushrooms and cook until browned.
Add in the lentils, mustard, smoked paprika, and soy sauce. Add 3 cups of broth. Simmer over medium heat for about 40 minutes, until the lentils are tender. Stir occasionally and add a bit of water if it becomes too dry.
When the lentils are cooked, stir in the coconut milk and season with salt and pepper to taste.